HWK 1 (4)

CBE 504 Homework #1 Due February 8, 2016 by 5pm (You (You may work in groups on the homework but the solutions should be your own work. Consulting  past year’s year’s homework, homework, answer answer keys, or online solutions solutions is not allowed allowed and will will result in an automatic automatic 0 for the assignment.) 1. Consier !"e reersib$e reersib$e prou%!&'orma!ion prou%!&'orma!ion rea%!ion rea%!ion in an en(yme&%a!a$y(e en(yme&%a!a$y(e biorea%!ion) k 1 k 2 S + E ↔ ES ↔ E + P k &1 &1

k &2 &2

Dee$op a ra!e e*pression 'or prou%!&'orma!ion usin+ !"e uasi s!eay&s!a!e appro*ima!ion an s"ow !"a! vs  v [ S ] −  p [ P ]  K  p d [ P ]  K m v= = dt  [ S ] [ P ] + 1+  K m  K  p

( ) ( )

-"ere

 K m=

k −1+ k 2 k 1

 an

 K  p=

k −1 + k 2 k −2

 an

v s=k 2 [ E0 ]

 an

v p =k −1 [ E0 ]

.

2. "e en(yme, 'umarase, 'umarase, "as !"e 'o$$owin+ kine!i% kine!i% %ons!an!s) k 1 k 2 S + E ↔ ES → E + P k &1 &1 

&1 &1

w"ere k1  / 10   s 4 &1 k &1 &1/4.4 * 10  s k 2 / 10 s&1 a. -"a! is !"e a$ue o' !"e i%"ae$is %ons!an! 'or !"is en(yme3  b. ! ! an en(yme %on%en!ra!ion %on%en!ra!ion o' 10&6 , w"a! wi$$ be !"e ini!ia$ ra!e o' prou%! 'orma!ion a! a subs!ra!e %on%en!ra!ion o' 10 &3

. n in"ibi!or in"ibi!or 7 is ae !o !"e en(yma!i% rea%!ion rea%!ion a! a $ee$ o' 1.0 +$. "e 'o$$owin+ a!a were ob!aine 'or 9 m / .2 + :$.  s .0 20 .658 10 .4 6.6; .4 5 . 4 .28 .

.22;

2.5

a. s !"e in"ibi!or %ompe!i!ie or non%ompe!i!ie3  b. Fin 9 . 4. De%arbo*y$a!ion o' +$yo*a$a!e :7 by mi!o%"onria is in"ibi!e by ma$ona!e 7.
Glyox, S (mM)

0!2$ 0!&& 0! 0!$ 0!" 0!%$ 

Rate of CO2 evolution, v (mmoles/l-h) I= 0 I=!2" I=!#$ (mM) (mM) !02 0!%& 0!$" !&# 0!'% 0!%$ !"% !0# 0!'$ !'# !&  2!0' ! !2' 2! !'2 !&# 2!$ 2!% !'2

a. -"a! -"a! !ype !ype o' o' in"i in"ibi! bi!ion ion is !"is3 !"is3  b. De!ermine !"e %ons!an!s =m, 9 m>, an 9 . 5.  pes!i%ie in"ibi!s !"e a%!ii!y o' a par!i%u$ar en(yme, w"i%" %an !"ere'ore be use !o assay 'or !"e presen%e o' !"e pes!i%ie in an unknown samp$e. a. n !"e $abora!ory, !"e ini!ia$ ra!e a!a s"own in !"e !ab$e be$ow were ob!aine. -"a! !ype o' in"ibi!or %ompe!i!ie, un%ompe!i!ie, un%ompe!i!ie, non&%ompe!i!ie7 is !"e pes!i%ie3 pes!i%ie3 De!ermine !"e a$ues o' =ma*, 9 , an 9 .

 b. '!er '!er 50 m$ o' !"e same en(yme so$u!ion in par! a7 is mi*e wi!" 50 m$ o' 8*10&4  subs!ra!e an 25 m$ o' a !es! samp$e, !"e ini!ia$ ra!e obsere is 18 ?min. -"a! is !"e pes!i%ie %on%en!ra!ion in !"e !es! samp$e assumin+ no o!"er in" ibi!ors or subs!ra!es are presen!3